No real problem. By pure geometry, a spherical Earth would have dropped about 1,640 feet. This is if your eyeballs were at ground level, which is decidedly pessimistic.

By an established rule (1.225 x square root of viewing altitude in feet), one could see 50 miles to features on the ground from a viewing altitude of 1,665 feet. The tallest building in Chicago is the Sears Tower, at 1,451 feet.

There is, of course, refraction of the air (density gradient => refractive index gradient). Based on the effects for radio waves, the surface would have appeared to drop only 1280 feet. It is an old truism that by the time when the setting (or rising) sun is touching the horizon, it actually would be below the horizon from strict geometry. Refraction makes that much difference.

So, it is a combination of (1) how high the viewer is, and (2) how high are the features you are looking for. No mirage is necessary. For sure, 50 miles would be a practical limit.

I earned my two masters degrees in aeronautics and astronautics in the study of aerodynamic refraction effects, and became something of an expert in the analysis of radio/radar propagation refraction.